Equivalent Length vs. Minor Pressure Head Loss in Pipe and Duct Components
Minor pressure and head loss in pipes vs. equivalent length in tubes and duct systems.
Pressure loss in straight pipes or ducts are called the major, linear or friction loss. Pressure loss in components like valves, bends, tees and similar are called the minor, dynamic or local loss.
Minor loss can be significant compared to major loss. In fact  when a valve is closed or nearly closed  the minor loss is infinite. For an open valve the minor loss can often be neglected (typical for a full bore ball valve).
Minor Loss
The pressure drop or the minor loss in a component correlates to the dynamic pressure in the flow and can be expressed as
Δp_{minor_loss} = ξ p_{d }
= ξ ρ_{f} v^{2} / 2 (1)
where
p_{d} = dynamic pressure in fluid flow (Pa (N/m^{2}), psf (lb/ft^{2}))
Δp_{minor_loss} = minor pressure loss (Pa (N/m^{2}), psf (lb/ft^{2}))
ρ_{f} = density of fluid (kg/m^{3}, slugs/ft^{3})
v = flow velocity (m/s, ft/s)
The minor loss can be expressed as head water column by dividing the dynamic pressure with the specific weight of water
Δh_{minor_loss,w }= (ξ ρ_{f }v^{2 }/ 2) / γ_{w}
= (ξ ρ_{f }v^{2 }/ 2) / (ρ_{w} g)
= ξ ρ_{f} v^{2 }/ (2 ρ_{w} g) (2)
where
Δh_{minor_loss,w} = minor head loss as water column (m H2O, ft H2O)
γ_{w} = ρ_{w} g = specific weight of water or reference fluid (9807 N/m^{3}, 62.4 lb_{f}/ft^{3})
g = acceleration of gravity (9.81 m/s^{2}, 32.174 ft/s^{2})
 1 psf = 0.00694 psi (lb/in^{2})
Note!  in the equation above the head is related to water as the reference fluid. Another reference fluid can be used  like Mercury Hg  by replacing the density of water with the density of the reference fluid  check Velocity Pressure Head.
If the flowing fluid has the same density as the reference fluid  typical for a water flow  eq. (2) can simplified to
Δh_{minor_loss }= ξ v^{2 }/ (2 g) (2b)
where
Δh_{minor_loss }= minor head loss (column of flowing fluid) (m fluid column, ft fluid column)
Minor Loss Coefficient
The minor loss coefficient  ξ  values ranges from 0 and upwards. For ξ = 0 the minor loss is zero and for ξ = 1 the minor loss is equal to the dynamic pressure or head. The minor loss coefficient can also be greater than 1 for some components.
The minor loss coefficient can be expressed by rearranging (1) to
ξ = 2 Δp_{minor_loss} / (ρ_{f} v^{2}) (3)
The minor loss coefficient can alternatively be expressed by rearranging (2) to
ξ = 2 ρ_{w} g Δh_{minor_loss,w} / (ρ_{f} v^{2}) (4)
The dynamic loss in components depends primarily on the geometrical construction of the component and the impact the construction has on the fluid flow due to change in velocity and cross flow fluid accelerations.
The fluid properties  in general expressed with the Reynolds number  also impacts the minor loss.
Minor loss information about components are given in dimensionless form based on experiments.
 Minor Loss Coefficients for Piping and Tube Components
 Minor Loss Coefficients for Air Duct Components
Equivalent Length
The dynamic minor loss in a component can be converted to an equivalent length of pipe or tube that would give the same major loss.
Major loss in a fluid flow can be expressed as
Δp_{major_loss} = λ (l / d_{h}) (ρ_{f} v^{2} / 2) (5)
where
Δp_{major_loss} = major (friction) pressure loss in fluid flow (Pa (N/m^{2}), psf (lb/ft^{2}))
λ = DarcyWeisbach friction coefficient
l = length of duct or pipe (m, ft)
v = velocity of fluid (m/s, ft/s)
d_{h} = hydraulic diameter (m, ft)
ρ_{f} = density of fluid (kg/m^{3}, slugs/ft^{3})
If we want the minor loss to be equal to the major loss for a given equivalent length of pipe or duct  then
Δp_{minor_loss} = Δp_{major_loss, eq} (6)
or by combining (1) and (2)
ξ ρ_{f} v^{2} / 2 = λ (l_{eq} / d_{h}) (ρ_{f} v^{2} / 2) (6b)
where
Δp_{major_loss, eq} = equivalent major loss (Pa (N/m^{2}), psf (lb/ft^{2}))
l_{eq} = equivalent pipe length (m, ft)
(6b) can be reduced and rearranged to express equivalent length as
l_{eq} = ξ d_{h} / λ (7)
The total head loss in a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems  plus the sum of the equivalent lengths of all components in the system.
Example  Equivalent Length of Gate Valve
The equivalent length of a 50 mm gatevalve with loss coefficient 0.26 when 1/4 closed located in a steel pipe with friction coefficient 0.03 can be calculated with (7) as
l_{eq} = 0.26 (0.05 m) / 0.03
= 0.4 m
Example  Duct Elbows
Additional equivalent length of 90^{o} duct elbows:
Duct Diameter (in)  Additional equivalent length (ft)  

90^{o} smooth elbow  90^{o} 5piece elbow  90^{o} 3piece elbow  
3  2.3  3  6 
4  3  4  8 
5  3.8  5  10 
6  4.5  6  12 
7  5.3  7  14 
8  6  8  16 
9  9  18  
10  10  20 
Related Topics

Fluid Flow and Pressure Loss
Pipe lines  fluid flow and pressure loss  water, sewer, steel pipes, pvc pipes, copper tubes and more. 
Fluid Mechanics
The study of fluids  liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
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